What are good alternatives to the expression "Artificial Intelligence"?
Artificial is said to derive from the Latin word "artificium" which connotes ideas such as crafting.  Thus, artificial is a correct usage, and algorithms can be regarded as "artifacts" in the context of information as opposed to physical manifestation of information (i.e. matter).  

However, I agree that the use of artificial is problematic in that, should strong Artificial General Intelligence ever be achieved, there is a stigma to "artificiality" that could have implications regarding personhood.  

My personal feeling is that we should be using:


Algorithmic Intelligence


which this is functional definition, and therefore more meaningful than "artificial".  Additionally, "algorithmic" is a neutral term, and provides a very accurate description of what these systems are. 



In terms of what is considered "intelligent", you may want to look at the concept of Bounded Rationality.  There is no hard definition of "intelligence", just degrees of optimality in regard to decision making in a condition of uncertainty. 

Because this is subjective for any problem that is not solved, modifiers are utilized, and thus we refer to AI as "strong" or "weak". These terms are also used to describe the degree to which certain types of problems (for instance a non-chance, perfect information game like Checkers) has been solved. Complexity theory will shed more light on this concept. 

For more insight on "artificial", you might find this question on the philosophical origin of the Turing Test interesting, because it partly involves the meaning of a "thing". (There were multiple words for this in Ancient Greek.)